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- Felix Lazebnik, Raymond Viglione
- Journal of Graph Theory
- 2002

Let n be an integer and q be a prime power. Then for any 3 ≤ n ≤ q − 1, or n = 2 and q odd, we construct a connected q-regular edgebut not vertextransitive graph of order 2qn+1. This graph is defined via a system of equations over the finite field of q elements. For n = 2 and q = 3, our graph is isomorphic to the Gray graph.

- Felix Lazebnik, Raymond Viglione
- Discrete Mathematics
- 2004

Let q be a prime power and k ≥ 2 be an integer. In [2] and [3] it was determined that the number of components of certain graphs D(k, q) introduced in [1] is at least qt−1 where t = b k+2 4 c. This implied that these components (most often) provide the best-known asymptotic lower bound for the greatest number of edges in graphs of their order and girth. In… (More)

Let q be a prime power, Fq be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(g, h, k,m) is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over Fq, with two vertices (p1, p2) ∈ P and [ l1, l2 ] ∈ L being adjacent if and only if p2 + l2 = p1l 1 . We prove that graphs… (More)

- Vasyl Dmytrenko, Felix Lazebnik, Raymond Viglione
- Journal of Graph Theory
- 2005

Let q be a prime power, Fq be the field of q elements, and k;m be positive integers. A bipartite graph G 1⁄4 Gqðk;mÞ is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over Fq, with two vertices ðp1;p2Þ 2 P and 1⁄2 l1; l2 2 L being adjacent if and only if p2 þ l2 1⁄4 p 1 l 1 . We prove that graphs… (More)

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